How Do I Solve Problems on Rotational Kinetic Energy and Center of Mass?

[ic3man]

2 probs: Rotational Kinetic Energy & Center of Mass

Got these questions wrong on a previous test. Have a final coming up soon and i would like to be able to understand these questions:

Homework Statement

1. Two masses, m1 = 2Kg and m2 = 4 Kg are thrown horizontally with the same speed of v = 10 m/s to strike and get attached at the two ends of a uniform rod of length L = 10m, pivoted at its center of mass. The rod is capable of rotation in the horizontal plane. The masses strike the rod at the same time. The mass of the rod is M = 2 Kg. Calculate the rotational kinetic energy of system after the collision.

2. A thin cylinder of radius R and length L has a non-uniform density given by p = p0 (x/L) but uniform along the radial direction. Calculate the location of the center of mass Xcm

(p0 in the previous problem is P null, which i assume is a constant)


2. The attempt at a solution

1. I didnt even know where to begin with this one

2. If this was a uniform rod, not a cylinder i could get the answer, but i wasnt sure if i had to take into consideration that it was a cylinder. Typically in questions in my homework, it doesn't provide a rod that has R, so i was wondering if the fact that it was a cylinder was not important, althought the teacher did provide the formula for the volume of a cylinder on the test.


Thanks for all the help. Couldnt figure out these questions on a previous test and i don't desire getting similar ones wrong on the final.

 

[OlderDan]

For #1 the final motion will be governed by conservation of angular momentum. A lot of mechanical energy will be lost in the process. You need to find the angular momentum of each ball about the pivot point. Any vertical momentum will be overcome by the vertical forces holding the rod in place, so you can neglect any vertical velocities acquired from gravity

For #2 you don't really need to know that it is a cylinder. By symmetry, the CM is on axis. A tapered rod that has the same mass distribution along its length would give you the same result.